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(D) The current $I$ is defined as the rate of flow of charge: $I = \frac{dQ}{dt}$.Given $Q = at - bt^2$,differentiating with respect to $t$ gives $I =

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Only $B$

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(D) The current $I$ is defined as the rate of flow of charge: $I = \frac{dQ}{dt}$.Given $Q = at - bt^2$,differentiating with respect to $t$ gives $I = a - 2bt$.$(i)$ Since $I = a - 2bt$,the current decreases linearly with time. Thus,statement $(A)$ is correct.$(ii)$ The current starts at $I = a$ at $t = 0$ and decreases continuously. It does not reach a maximum after $t = 0$. Thus,statement $(B)$ is incorrect.$(iii)$ Setting $I = 0$,we get $a - 2bt = 0$,which implies $t = a/2b$. Thus,statement $(C)$ is correct.$(iv)$ The rate of change of current is $\frac{dI}{dt} = \frac{d}{dt}(a - 2bt) = -2b$. Thus,statement $(D)$ is correct.Since only statement $(B)$ is incorrect,the correct option is $(D)$.

The charge flowing in a conductor varies with time as $Q = at - bt^2$. Then for current,which statement is incorrect?
$(A)$ decreases linearly with time
$(B)$ reaches a maximum and then decreases
$(C)$ falls to zero after time $t = a/2b$
$(D)$ changes at a rate $-2b$

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The charge flowing in a conductor varies with time as $Q = at - bt^2$. Then for current,which statement is incorrect?$(A)$ decreases linearly with time$(B)$ reaches a maximum and then decreases$(C)$ falls to zero after time $t = a/2b$$(D)$ changes at a rate $-2b$